Water Thresholds

The next time you fill a bathtub, once you’ve turned off the tap, wait until the water is still. Slip your hand into the water, slowly and gently, so that you make as little disturbance in the water as possible. Then move your hand through the water about as fast as a snail moves, and watch and feel how the water adapts to the movement, flowing gently around your hand.

Once you’ve gotten a clear sense of that gradually increase the speed with which your hand is moving. After you pass a certain threshold of speed, the movements of the water will take the form of visible waves – a bow wave in front of your hand, a wake behind it in which water rises and falls rhythmically, and wave patterns extending out to the edges of the tub. The faster you move your hand the larger the waves become, and the more visible the interference patterns as the waves collide with one another.

Keep on increasing the speed of your hand. You’ll pass a second threshold, and the rhythm of the waves will disintegrate into turbulence: the water will churn, splash and spray around your hand, and chaotic surges of water will lurch up and down the sides of the tub. If you keep it up, you can get a fair fraction of the bathwater on your bathroom floor, but this isn’t required for the experiment. Once you’ve got a good sense of the difference between the turbulence above the second threshold and the oscillations below it, take your hand out of the water, and watch what happens: the turbulence subsides into wave patterns, the waves shrink, and finally – after some minutes – you have still water again.

This same sequence of responses can be traced in every complex system, governing its response to every kind of disturbance in its surroundings. So long as the change stays below a certain threshold of intensity and rapidity – a threshold that differs for every system and every kind of change – the system will respond smoothly, with the least adjustment that will maintain its own internal balance. Once that threshold is surpassed, oscillations of various kinds spread through the system, growing steadily more extreme as the disturbance becomes stronger, until it passes the second threshold and the system’s oscillations collapse into turbulence and chaos. When chaotic behavior begins to emerge in an oscillating system, in other words, that’s a sign that real trouble may be sitting on the doorstep.